A couple of weeks ago, we described the battle between Honda and Toyota for the emerging small hybrid segment. Compacts with battery packs and motors could become the most affordable and highest MPG cars on the road—pushing hybrid technology deep into the mainstream market. Yet, the $19,200 Honda Insight and $20,000 Honda CR-Z are the closest cars so far to attempt a grab of the entry-level affordable compact hybrid market.

Toyota wants those cost- and fuel-conscious customers, especially in Europe where small cars rule. The company debuted the Toyota Yaris Hybrid at this week’s 2011 Geneva Motor Show—showing that it intends to downsize its proven full hybrid technology. The Yaris Hybrid is expected to go on sale in Europe next year. It’s still too early to know if it will come to the United States.

While Honda will utilize a mild form of gas-electric technology for its small hybrids, Toyota’s system is a full hybrid capable of moving the car down the road on electricity alone. According to Toyota, the company plans to bring full hybrid technology to all of its European models in the next decade. “Two years ago, 8 percent of European customers said they wanted their next vehicle to be a hybrid,” said Didier Leroy, President of Toyota Motor Europe. “Today that figure has doubled, to 16 percent.”

Unlike Honda’s existing mild hybrid technology–which might be a more immediate fit for small cars—Toyota engineers will need to work on packaging its electric system into a smaller space. That could mean reducing the size and weight of the battery pack used in current models. All systems will have to be optimized for the smaller format.

To help draw attention to the unassuming Yaris hybrid subcompact concept on display in Geneva, Toyota applied a solar panel to its roof. The solar panel could help power the car’s air-conditioning, making a modest improvement in overall fuel efficiency.